An exact analytical treatment of the dynamical problem for time-dependent 2 × 2 pseudo-Hermitian su(1, 1)
Hamiltonians is reported. A class of exactly solvable and physically transparent scenarios are identified within
both classical and quantum contexts. The class is spanned by a positive parameter ν that allows for distinguishing
two different dynamical regimes. Our results are usefully employed for exactly solving a classical propagation
problem in a guided wave optics scenario. The usefulness of our procedure in a quantum context is illustrated
by defining and investigating the su(1, 1) “Rabi” scenario, bringing to light analogies and differences with the
standard su(2) Rabi model. Our approach, applied to the generalized von Neumann equation describing open
quantum systems through non-Hermitian Hamiltonians, succeeds in evidencing that the ν-dependent passage
from a real to a complex energy spectrum is generally unrelated to the existence of the two dynamical regimes.